Question: Harper uploaded a funny video of her dog onto a website. The relationship between the elapsed time, $d$, in days, since the video was first uploaded, and the total number of views, $V(d)$, that the video received is modeled by the following function. $V(d)=4^{{1.25d}}$ How many views will the video receive after $6$ days? Round your answer, if necessary, to the nearest hundredth.
Thinking about the problem We want to find the number of video views received after $6$ days. In other words, we are given a $d$ value of $6$ days and want to find the number of video views associated with that input, or $V(6)$. To do this, we can substitute ${6}$ in for $ d$ and evaluate. V ( 6 ) = 4 1.25 ( 6 ) V( {6})=4\^{1.25({6})} Evaluating the expression We can evaluate the expression as shown below. V ( 6 ) = 4 1.25 ( 6 ) = 4 7.5 = 32,768 \begin{aligned}V(6)&=4\^{1.25(6)}\\\\ &=4^{{7.5}}\\\\ &=32{,}768\\\\ \end{aligned} After $6$ days, the video will receive $32{,}768$ views.